Find the arc length (s) of the curve r(t) = (est, -2e5t, 3e5t) for 0 ≤ t ≤ In (2) 8=

Q: In this question, consider the vectors 10 8 V1 ~- - ( ) - ~- - ( ) - - - () ---- () v2 = V3 = b and…

A: The objective of the question is determine the coefficient matrix" A" without simplifying.

Q: 1.2: The solution of (Se*-3)³ = 32 is a) In 3 b) 2 c) 1 do e) None of the above

A: Explanation of the answer is as follows

Q: 8. Evaluate F. dr using Stoke's theorem when F = (2xy — x²)ī — x² − y² )ī and C is the boundary of…

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Q: An arithmetic sequence begins 7, 13, 19, 25, 31, ... (a) Find the common difference d for this…

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Q: Solve the differential equation dy dx y+√√x²+y² X O a. y² = 2x-1 O b. x2 = 2y-1 O c. √x² + y² O d.…

A: To solve the given differential equation.

Q: Find the indefinite integral. Remember to include a "+ C" if appropriate. (2423-4x) dx = [

A: Here we will solve the indefinite integral,

Q: The weekly marginal cost of producing x pairs of tennis shoes is given by the following function,…

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Q: dr √3-4r-r² 17 -1 r+2 sin-¹( + ²) + C +C) (Ans: sin

A: Yes the answer you have given is correct. see below the calculation using the  trigonometric…

Q: Find the integrating factor μ(x) of y' + 4y - tan(x) = 0 such that μ(0) = 1. μ(x) =

A: See the details solution in below

Q: (a) Find the rank of the following matrix for all values of a 1 a -1 2 2 -1 a 5 1 10 -61 Show your…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 6. Determine the 19th derivative of the function y=sin(x). Fully explain the process you used to…

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Q: Find foda + C

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Q: Find the absolute maximum and minimum, if either exists, for f(x)=x² - 6x + 6. Find the first…

A: We have to find absolute maxima and minima of given function.

Q: Solve the differential equation [x a. b. C. d. y tan ¹()] 2x tan-¹(²) -¹ (²/2) dx + x tan¯¹ (²/2)dy…

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Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

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Q: Problem 7. (1 point) Find a solution to A(t) = dt 9A if A(0) = 3. help (fo

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Q: 3. a. Solve the differential equation y'= 2x√/1-y² b. Explain why the initial value problem y'=…

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Q: (a) Consider the power series Show that B(x) converges for all x. B(x) = Σ n=0 (-1)η 2η 22n (n!) ²

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Q: A region is bounded by the curve y^2 =4x  and the line x=y Find the distance of the centroid of the…

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Q: 1. Find the derivatives of each of these functions: a. y = ln (4x² + 4) b. y = 22² c. y = 25x+7…

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Q: T/F: The half-life of the exponential function P(t) = et is T = ln(2).

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Q: Q2. Find the second order partial derivative of x² - y² + 2xz - xy + yz.

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Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 6y² + 6z² and x…

A: To evaluate the triple integral ∬∫ExdV where E is the solid bounded by the paraboloid…

Q: A store sells two brands of camping chairs. The store pays $10 for each brand A chair and $20 for…

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Q: Let v = 27 + 3 + 5k. Find ||||. Check Answer

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Q: Given x = y² +y + 1 from 0≤y=2 The Arc Length of the given curve over the interval is a. 7.38 units…

A: I have stated the used formula in the solution

Q: Q3. Find the distance between the points AB and BC where A is (2,1,0), B is (-1,3,1) and C is (-1,…

A: The points A2,1,0, B-1,3,1 and C-1,0,1 we have to find the distance between the points AB and BC…

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: 4. Let f(x, y) = y²exy (a) Find the normal vector to the graph of f(x, y) at (0,1,1). (b) Find the…

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Q: Evaluate the definite integral using Part 1 of the Fundamental Theorem of Calculus. 6² Enter the…

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Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: Let f be the function graphed below. If 20 subintervals of equal length are used, write a summation…

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Q: Use calculus to find the open intervals on which the function f (x) = x +4√1 − x is increasing or…

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Q: Find a vector with initial point (4, -4,0) and terminal point (7, -14, - 10). Then find a unit…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the partial sum S, of the geometric sequence that satisfies the given conditions. 2 a=²₁r = ₁ n…

A: Please see the below picture for detailed solution.

Q: B A 876, 5432 -10-9-8-7-6 -54 -3 -2 -1 1234 -1 Graph of f D 1 2 3 4 5 6 7 8 9 10 C x.

A: We will find the required.

Q: Consider the vector whose initial point is P(-6, 1) and terminal point is Q(-5, -3). Find the…

A: We need to find vector.

Q: Let f be the function graphed below. If 20 subintervals of equal length are used, write a summation…

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Q: Differentiate the following function. You do not need to simplify the derivative. dy dx || y = 2e²²

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Q: Determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 4 8 16…

A: Topic = Sequence

Q: Let f(x) = 4x + 7 – 17e². Then the equation of the tangent line to the graph of f (0, -10) is given…

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Q: se the limit definition to find the instantaneous rate of change of f(x) = 3x^2 - 4x at x= -3.

A: The instanteneous rate of change of a function f(x) at x=a is the limit of the average rate of…

Q: Find the integral of f(x) = e- sinh(x) between 0 and 1.

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Q: Q-3: a) b). Using logarithmic differentiation, find the derivative of -3x√2x-5 (6-5x)4 - 34x = 0.…

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Q: Let à = (-2, 2, 3) and 6 = (4, - 1,5). Find the projection of b onto a. proj, b =< Check Answer

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Q: Allouette Shipping Company has a peculiar fee schedule. When determining the price to ship a…

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Q: Use L'Hopital rule, find the following limit? lim (4x + 1) cotx x→0+

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Q: əz 7. Find the partial derivatives and if: əz əx ду (a) z = x-y r2 + 1² (x, y) = (0,0) = x² sin(x-y)…

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Q: Consider the vector whose initial point is P(-6, 6) and terminal point is Q(5, 3). Find the position…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find the area S of the shaded region in the figure if ƒ (0) = 0² + 30. Note that 0 varies from 0 to…

A: To find the are S of the shaded region in the figure if fθ=θ2+3θ Note that θ varies from 0 to…